MATLAB - piecewise defined Fn as periodic

[Apothus]

Homework Statement

We have been provided with a graph
of a function modeled by F(t)=a-aU(t-1)+(-3/2.5*t+4.2)U(t-1)-(-3/2.5*t+4.2)U(t-3.5)

I have entered this into MATLAB and it replicates the graph we have been provided with but we now need to extend this as an Even function.

 

[LCKurtz]

Can't you just use F(-t) = F(t)?

What are you going to do next with this function?

 

[Mene]

I would first clarify the meaning of an "Even function" in this context. An Even function is a mathematical function that satisfies the condition f(-x) = f(x) for all values of x. This means that the graph of the function is symmetric about the y-axis.

To extend the given piecewise defined function as an Even function, we can add a term that is the mirror image of the existing terms about the y-axis. This can be achieved by replacing t with -t in the original function. The resulting function would be F(t) = a - aU(-t-1) + (-3/2.5*(-t)+4.2)U(-t-1) - (-3/2.5*(-t)+4.2)U(-t-3.5).

In MATLAB, this can be represented as:

F = @(t) a - a*heaviside(-t-1) + (-3/2.5*(-t)+4.2)*heaviside(-t-1) - (-3/2.5*(-t)+4.2)*heaviside(-t-3.5)

This new function will have the same graph as the original function but will also be symmetric about the y-axis, making it an Even function. Additionally, since the original function was periodic with a period of 2.5, the extended Even function will also be periodic with the same period.

In conclusion, by adding a term that is the mirror image of the existing terms about the y-axis, we can extend the given piecewise defined function as an Even function while preserving its periodicity.